Yes.
Both free gifts and volume discounts run through the unified discount function. They stack natively, subject to Shopify's combination rules.
Why this works
The unified function evaluates every discount type in a single pass. There's no "fight" between two separate functions — one function applies them all in the right order.
Combination rules
To allow them to combine with discount codes too, configure combinations in Shopify admin: Discounts → (your discount) → Combinations.
Example
A customer buys 3 t-shirts ($75 cart):
Volume discount: "Buy 3+ → 10% off" applies → $67.50.
Free gift threshold ($50): also crosses → free tote added.
Free shipping threshold ($50): also crosses → shipping waived.
All three apply to the same order.